We detailed above an approximation of \(\)  using its entropic regularized version \(_{\epsilon }\) .
By analogy with the debiasing performed in [1]}, [2]} and detailed in Section REF , it is a natural question to ask if there is an entropic bias (similar to \(\)  with \(\) , see Definition REF ), and if it needs to be corrected.
Providing answers on this problem for \(_{\epsilon }\)  is difficult due to the non-convexity of the formulation, and remains an open problem.
To provide a partial answer, we detail results from [3]} on the asymptotic \(\epsilon \rightarrow \infty \) , for balanced \(\) .
We now write the distortion \(k(d_(x,x^{\prime }), d_(y, y^{\prime }))\)  instead of \(|d_(x,x^{\prime }) - d_(y, y^{\prime })|\) , where \(k\)  is a kernel defined on \(\) , which is a more general expression than Definition REF .
Typically, we take \(k(x,y) = |x-y|^p\)  where \(1\le p<2\) .
We start with a result on the limit of \(_{\epsilon }\)  when \(\epsilon \rightarrow \infty \) .
